Almost purity for overconvergent Witt vectors
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Almost purity for overconvergent Witt vectors. / Davis, Christopher James; Kedlaya, Kiran.
In: Journal of Algebra, Vol. 422, 2015, p. 373-412.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Almost purity for overconvergent Witt vectors
AU - Davis, Christopher James
AU - Kedlaya, Kiran
PY - 2015
Y1 - 2015
N2 - In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite étale extension of R[p−1]R[p−1] is “almost” finite étale over R . Here, we use almost purity to lift the finite étale extension of R[p−1]R[p−1] to a finite étale extension of rings of overconvergent Witt vectors. The point is that no hypothesis of p-adic completeness is needed; this result thus points towards potential global analogues of p -adic Hodge theory. As an illustration, we construct (φ,Γ)(φ,Γ)-modules associated with Artin Motives over QQ. The (φ,Γ)(φ,Γ)-modules we construct are defined over a base ring which seems well-suited to generalization to a more global setting; we plan to pursue such generalizations in later work.
AB - In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite étale extension of R[p−1]R[p−1] is “almost” finite étale over R . Here, we use almost purity to lift the finite étale extension of R[p−1]R[p−1] to a finite étale extension of rings of overconvergent Witt vectors. The point is that no hypothesis of p-adic completeness is needed; this result thus points towards potential global analogues of p -adic Hodge theory. As an illustration, we construct (φ,Γ)(φ,Γ)-modules associated with Artin Motives over QQ. The (φ,Γ)(φ,Γ)-modules we construct are defined over a base ring which seems well-suited to generalization to a more global setting; we plan to pursue such generalizations in later work.
U2 - 10.1016/j.jalgebra.2014.08.055
DO - 10.1016/j.jalgebra.2014.08.055
M3 - Journal article
VL - 422
SP - 373
EP - 412
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -
ID: 64395690